Sunday 3 September 2023

On This Day in Math - September 3

If it's just turning the crank it's algebra,
but if it's got an idea in it, it's topology.

~Solomon Lefschetz

The 246th day of the year; 246 is a sphenic (wedge) composite since it is the product of three distinct prime factors, 246 = 2x3x41. (what would be the next sphenic number?)

246 is also equal to the sum  9C2 + 9C4 + 9C6 (9 choose 2,4,6)

246 = 233 + 13 (13th Fibonacci number plus 13) *Derek Orr@Derektionary

246 is the smallest number whose complete factorization contains the first four digits (and no others) 246 = 2*3*41

Algebra Fact @AlgebraFact points out that: "Tao, et all, have proved that there are infinitely many primes 246 apart." On the way to proving, hopefully, that there are an infinity of twin primes.

246 is an untouchable number, a number that can not be formed from the proper divisors of any number. Paul Erdos proved there are an infinite number of them. The early ones are 2, 5, 62, 88, 96... There are only 29 untouchable year dates, but very unevenly divided by the century groups. 5 below 100, 5 more before 200, then 12 between 200 and 300, and 8 between 300 and 400.

246 is a palindrome in base 5(1441) and base 9(303)

246 can be expressed as the sum of three (not distinct) squares. 14^2 + 5^2 + 5*2

The "aliquot sequence" of a number is the chain of results following from iterating the sum of the aliquot factors. The Chain for 246 is 258, 270, 450, 759, 393, 135, 105, 87, 33, 15, 9, 4, 3, 1, 0. *Wikipedia

EVENTS

1457  Georg Peurbach observed a lunar eclipse from a site near Vienna. He measured the duration of the eclipse and then found the time of the midpoint. It was eight minutes earlier than the time predicted by the Alphonsine Tables.These tables, prepared in Toledo, Spain, for King Alfonso X, were completed in 1252. Based on Ptolemy's theory, they represented the best data available in Peurbach's time. Peurbach produced a new collection of tables of eclipse calculations in Tabulae Ecclipsium which he completed around 1459. When he observed eclipses on 3 July and 27-28 December 1460 he was able to compare the times with the predictions contained in his own tables.

image  Georg von Peuerbach: Theoricarum novarum planetarum testus, Paris 1515

1752 The dates 3 to 13 September did not exist in England in 1752 due to the conversion to the Gregorian calendar. Poor Richard’s Almanac for 1752 carried the catchy heading, “September hath XIX days.” Much of Europe made the change in 1582, and since 1600 was a leap year under the Gregorian but not the Julian calendar, England had to omit eleven days, not ten. *VFR England and the American Colonies dropped the Roman era Julian Calendar, which had become 10 days out of synchrony with the solar cycle, and adopted the Gregorian Calendar. People rioted in the streets thinking the government stole 11 days of their lives. Instituted by Pope Gregory XIII in 1582, the calendar has 365 days with an extra day every four years (the leap year) except in years divisible by 100 but not divisible by 400. Thus, the calendar year has an average length of 365.2422 days. It moved the day's date up from September 3rd to September 14th. Some other countries, including Russia, did not change until the twentieth century.*TIS

1803 John Dalton makes the first entry in his first meteorological notebook. Dalton came to his views on atomism through his interest in meteorology. The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816.  By September 3, 1803 he made a logbook entry that day titled, “Observations on the Ultimate Particles of Bodies and their Combinations.” It was the first use of symbols to represent the elements of modern chemistry.

1806 Francois Arago and Jean-Baptiste Biot leave Paris for Spain to finish the measurement of the Paris Meridian.  Arago had been picked to head the completion of the task while a 19yr old student at the Ecole Polytechnique.  He was nominated by his professor, Dennis Poisson and appointed on Feb 2, 1805 to finish the work began by Mechain and Delambre.  *Amir D Aczel, Pendulum, pg 75-78

François Arago was sent to the municipal college of Perpignan, where he began to study mathematics in preparation for the entrance examination of the École Polytechnique. Within two years and a half he had mastered all the subjects prescribed for examination, and a great deal more, and, on going up for examination at Toulouse, he astounded his examiner by his knowledge of J.-L. Lagrange 's work.

Towards the close of 1803, Arago entered the École Polytechnique, Paris, but apparently found the professors there incapable of imparting knowledge or maintaining discipline. The artillery service was his ambition, and in 1804, through the advice and recommendation of Siméon Poisson, he received the appointment of secretary to the Paris Observatory. He now became acquainted with Pierre-Simon Laplace, and through his influence was commissioned, with Jean-Baptiste Biot, to complete the meridian arc measurements which had been begun by J. B. J. Delambre, and interrupted since the death of P. F. A. Méchain in 1804 *WIK

 Arago by Charles de Steuben, *Wik

1806 F. Nichols sends a copy of his printing of Playfair's Geometry to Thomas Jefferson.
"Sir,—
I desire you to accept a copy of Playfair’s Geometry, which I reprinted last winter.
The corrections of grammatical inaccuracies, &. mentioned in the Advertisement, occur after Book I. There are few corrections in Book I.
The book is pretty correctly printed. The principal typographical errors appear at the end of the volume.
Some improvements will be made in another edition, if indeed another edition should ever be wanted.
Playfair’s Geometry is adopted at Cambridge in Massachusetts, Newhaven in Connecticut, & in a few private places of education. I have been informed that it will be introduced into other colleges.
It is a circumstance unfriendly to the reception of a new elementary work of science, designed for the use of students, that some teachers are unwilling to introduce any book into their seminaries, which they have not read at school or college.
I am, with respect, Sir, Your obedient Servant,
F. Nichols."
Jefferson would reply with thanks on 19 Sept.  *Natl. Archives
advertising in the Apr. 7, 1795, issue of the Massachusetts Mercury as "Francis Nichols, late professor of mathematics in the new college at Manchester"; author and bookseller at Philadelphia, 1802-14; member of the American Philosophical Society; bookseller at New York City, 1817-20)*Library of Congress

I have a copy of John Playfairs Geometry printed in 1804 in Edinburgh by Bell & Bradfute.  It was signed on the flyleaf by James Norgate, Caius College Cambridge in 1604.  On the inside of the coverit is signed by Pro James Boyst.  Below his signature is written, "Nov 7, 1946, Lord Plimton (unclear) bought this bookoff Plummer the Carpenter who bought it at the Boyst sale."

1821 A Hurricane made landfall on this day in New York City and moved north into Connecticut. It would confuse and inspire William Redfield, and become the first hurricane tracked from beginning to end. While reviewing the storm damage on horseback across Connecticut Redfield noticed that trees in the northern parts of the state fell in the opposite direction from those he had witnessed further south. His interest led him to make a careful study of newspaper reports, letters and ships log an document the storm from beginning to end. He concluded, "This storm was exhibited in the form of a great whirlwind." Redfield was the first to give evidence to support that hurricanes are large circular vortexes. His study of this and other storms led to the classic meteorology paper, "On The Prevailing Storms of the Atlantic Coast." John Farrar had made similar observations describing the hurricanes as “a moving vortex and not the rushing forward of a great body of the atmosphere”, after the Great September Gale of 1815..*Wik

1822 A wagon train containing three tons of books arrived at Allegheny College in Meadville, PA. They came from one of the ﬁnest private libraries in America, that of James Winthrop. He was a descendant of John Winthrop, ﬁrst governor of the Massachussettts Bay Colony. His father was Professor of Mathematics and Natural Philosophy at Harvard and so the collection contained a number of important mathematical works. Winthrop was upset that Harvard had not given him an honorary degree and so he gave the books to Allegheny. [Allegheney College Alumni Bulletin, June 1933.] *VFR

It was, in a sense, Allegheny’s first capital campaign, and our first transformative gift. And it put Allegheny on the national map. Allegheny’s first President, Timothy Alden, in 1824 received an unsolicited letter, congratulating the College on its “good fortune of having become the objects of donations so liberal.”

“I had not expected there was such a private collection in the U.S.,” the author wrote. “We are just commencing the establishment of a University in Virginia but cannot flatter ourselves with the hope of such donations as have been bestowed on you.”

The letter was written by former President Thomas Jefferson. Dated Feb. 14, 1824, and penned from Monticello, the letter remains in the Pelletier Library Archives today.

In 2000, NASA data showed the hole at just under 11 million square miles - the biggest it had ever been. Record low temperatures in the stratosphere are believed to have helped the expansion of the ozone hole during the southern hemisphere’s spring season. Antarctic ozone depletion starts in July, when sunlight triggers chemical reactions in cold air trapped over the South Pole during the Antarctic winter. It intensifies during August and September before tailing off as temperatures rise in late November of early December. Depletion of the ozone layer over Antarctica and the Arctic is being monitored because ozone protects Earth from harmful ultraviolet radiation. By 9 Sep 2000, the hole had grown over Chile, exposing a populated city for the first time. Image, compiled from NASA's Total Ozone Mapping Spectrometer instrument onboard the Earth Probe satellite, reveals how the ozone hole (in deep blue) has extended as far as southern Chile. *TIS

2009 Saturn's rings cross the plane of the Earth's orbit. This was the first such crossing since May 22, 1995, and another will not occur until March 23, 2025. *Wik

This sequence of images from the Hubble telescope documents a rare astronomical alignment: Saturn's magnificent ring system turned edge-on. This event occurs when the Earth passes through Saturn's ring plane, as it does about every 15 years.

BIRTHS

1780 Heinrich Christian Schumacher (September 3, 1780 – December 28, 1850)
Schumacher was a German astronomer. He was director of the Mannheim observatory from 1813 to 1815, and then became professor of astronomy in Copenhagen. From 1817 he directed the triangulation of Holstein, to which a few years later was added a complete geodetic survey of Denmark (finished after his death). For the sake of the survey an observatory was established at Altona, and Schumacher resided there permanently, chiefly occupied with the publication of Ephemerides (11 parts, 1822–1832) and of the journal Astronomische Nachrichten (founded by himself in 1821 and still being published), of which he edited thirty-one volumes. *TIA

1814 James Joseph,(Sylvester) (3 Sep 1814; 15 Mar 1897) youngest child of Abraham Joseph, born in London. The eldest son, an actuary, eventually migrated to the U.S. where, for unknown reasons, he took the surname Sylvester. The rest of the family soon followed suit, so that is how James Joseph Sylvester got his name. *VFR British mathematician who, with Arthur Cayley, founded the theory of algebraic invariants, algebraic-equation coefficients that are unaltered when the coordinate axes are translated or rotated. Beginning in 1833, he studied at St John's College, Cambridge. However, at this time signing a religious oath to the Church of England was required to graduate. Being Jewish, he refused and so he did not graduate. He taught physics at the University of London (1838-41), one of the few places which did not bar him because of his religion. Sylvester did important work on matrix theory, in particular, to study higher dimensional geometry. In 1851 he discovered the discriminant of a cubic equation. Earlier in his life, he tutored Florence Nightingale.*TIS (This idea of Sylvester tutoring Nightingale, to the best of my knowledge, originates from the Herbert Baker obituary. Karen Hunger Parshall, among others, has questioned the accuracy of this statement.)
He was instrumental in shaping graduate study and American mathematics in the later half of the 19th century as a professor at the Johns Hopkins University and as founder of the American Journal of Mathematics. *Wik
James Joseph Sylvester died, at age 83, after earlier suﬀering a paralytic stroke while working at his mathematics. *VFR
I came across a nice story about Sylvester on the wonderful "Cut-the-Knot" blog of Alexander Bogomolny. He writes, "Sylvester was one the greatest British mathematicians of the 19th century. He was known for his absentmindedness and poor memory; on one occasion he even denied the truth of one of his own theorems. "

1869 Austrian chemist Fritz Pregl (3 September 1869 – 13 December 1930) Pegl began research on bile acids in 1904. With only tiny yields to study, he pioneered micro analytical techniques and designed a new balance capable of weighing 20 grams to an accuracy of 0.001 milligrams. Pregl was awarded the Nobel Prize in Chemistry 1923 for his efforts *RSC.org
In 1950, the department of the University of Graz where Fritz Pregl had worked was named the Institute of Medical Chemistry and Pregl Laboratory. Streets in Graz, Innsbruck, Vienna and Klagenfurt were named after him. In Slovenia, Pregl Awards have been bestowed annually since 2007 by the National Institute of Chemistry for the research work and for outstanding doctorates. Slovenian pupils are conferred Pregl Recognition Awards, whereas secondary school students are conferred Pregl Citations for excellent results in national competitions in chemistry. A square in Ljubljana is named after Pregl. The Fritz Pregl Prize has been awarded annually since 1931 in chemistry by the Austrian Academy of Sciences from the funds left at its disposal by Pregl. *Wik

1874 Fredrik (Carl Mülertz) Størmer (3 Sep 1874; died 13 Aug 1957) was a geophysicist and mathematician who developed a mathematical theory of auroral phenomena. An aurora is the light emitted by energetic protons and electrons at the top of Earth's atmosphere when they come in contact with solar wind particles. He also contributed both important photographic observations and mathematical data to the understanding of the polar aurora, of stratospheric and mesospheric clouds, and of the structure of the ionosphere. The discovery of the Van Allen Radiation Belts by James Van Allen confirmed with surprising accuracy Størmer's theoretical analysis of solar charged particle trajectories in Earth's magnetic field.*TIS

1884 Solomon Lefshetz (3 September 1884 – 5 October 1972) born in Moscow. He invented the phrase “algebraic topology.” See A Century of Mathematics in America, Part I, 1988, p. 171. *VFR mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.*Wik

1905 Carl David Anderson (3 Sep 1905; 11 Jan 1991)American physicist who, with Victor Francis Hess of Austria, won the Nobel Prize for Physics in 1936 for his discovery of the positron, or positive electron, the first known particle of antimatter. He examined the photographs of cosmic rays taken as they passed through a Wilson cloud chamber in a strong magnetic field. Besides the curved paths of negative electrons, he found also paths deviating in the opposite direction, corresponding to positively charged particles - yet having the the same mass as an electron! Previously, Dirac had predicted such particles by theoretical solution to electromagnetic field equations. *TIS

 *wik

1970 Stanislav Konstantinovich Smirnov (3 September 1970 - ) is a Russian mathematician currently working at the University of Geneva, who was awarded the Fields Medal in 2010. His research focuses on the fields of complex analysis, dynamical systems and probability theory. *Wik

DEATHS

1595 Federico Commandino (1509 – September 5, 1575) died on this day. “In the sixteenth century, Western mathematics emerged swiftly from a millennial decline. This rapid ascent was assisted by Apollonius, Archimedes, Aristarchus, Euclid, Eutocius, Hero, Pappus, Ptolemy, and Serenus—as published by Commandino,” *VFR He translated the works of ancient mathematicians and was responsible for the publication of the works of Archimedes. He also translated the works of Aristarchus of Samos (On the masses and distances of the Sun and the Moon), Pappus of Alexandria (Mathematical collection), Hero of Alexandria (Pneumatics), and Euclid (Elements). Among his pupils was Guidobaldo del Monte. Commandino maintained a correspondence with the astronomer Francesco Maurolico.
The proposition known as Commandino's theorem** first appears in his work on centers of gravity, Liber de centro gravitatis solidorum in 1565. *Wik
**The four medians of a tetrahedron concur in a point which divides each tetrahedron median in the ratio 1:3, the longer segment being on the side of the vertex of the tetrahedron. Student's should compare this to the property of the medians of a triangle which concur at a point that divides the meadian in a 1:2 ratio.

1910 Wilhelm Winkler (29 June 1884 in Prague, Bohemia (Austro-Hungarian Empire, now Czech Republic - 3 Sept 1984 in Vienna, Austria) After attending the trading high school in Gera, Winkler worked as a merchant in Eisenberg, following in the footsteps of his grandfather. In 1875 he gave up this trade and devoted his time entirely to astronomy. Advised by Carl Bruhns, director of the Leipzig University Observatory, he established an observatory on his estate in Gohlis near Leipzig. From 1878 Winkler regularly observed sunspots; other fields of his observational interests were comets, occultations of stars by the Moon, and Jupiter's satellites. *Uni Bonn Web page

1967 William P Milne (22 May 1881 in Longside, Aberdeenshire, Scotland - 3 Sept 1967 in Glack, Aberdeenshire, Scotland) studied at Aberdeen and Cambridge universities. He taught at Clifton College and then became Professor of Mathematics at Leeds. He published papers in Geometry including many in the Proceedings of the EMS. *SAU (Not to be confused with the William J Milne who, as President of the New York State Normal School in Albany, wrote many popular textbooks in arithmetic, algebra and geometry for high school use)

1992 Barbara McClintock (16 Jun 1902, 3 Sep 1992) American scientist regarded as one of the most important figures in the history of genetics. In the 1940s and 1950s McClintock's work on the cytogenetics of maize led her to theorize that genes are transposable - they can move around - on and between chromosomes. McClintock drew this inference by observing changing patterns of coloration in maize kernels over generations of controlled crosses. The idea that genes could move did not seem to fit with what was then known about genes, but improved molecular techniques of the late 1970s and early 1980s allowed other scientists to confirm her discovery. She was awarded the 1983 Nobel Prize in Physiology or Medicine, the first American woman to win an unshared Nobel Prize. *TIS

 *Wik

1995 Bent Christiansen From his Obituary: "Bent was a legend in mathematics education in Denmark and the Nordic countries. His impact on the development of the teaching and learning of mathematics in primary and lower secondary education can hardly be over-estimated. He wrote textbooks and books on mathematics education, especially the very influential 'Goals and means in basic mathematics education' ('Mål og midler I den elementære matematikundervisning', 1967). He gave innumerable in-service courses and invited lectures at meetings and conferences. Naturally, he also served on hosts of national committees, including the Danish National Sub-Commission of ICMI (1961-1972). All this earned him a reputation as a charismatic, enthusiastic and extremely energetic mentor for generations of mathematics teachers, teacher trainers and colleagues."

247 = 50123 - 49876

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell